Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
318 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. #16840651 | C4 | semidirect |
| 13. C4×#11758187 | C4 | semidirect |
| 17. C4⋊#11758185 | C4 | semidirect |
| 18. #16839580 | C4 | semidirect |
| 19. C61×C4⋊C16 | C4 | semidirect |
| 70. #11758187 | C4⋊C4 | semidirect |
| 104. C4×C61 | #347 | semidirect |
| 130. C4⋊C16 | #6923 | semidirect |
| 135. C61 | #12666 | semidirect |
| 223. C4 | #16840652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840652 | 2 |
| C4×#14519852 | 2 |
| #21461613 | 2 |
| #21460859 | 2 |
| #21447573 | 2 |
| #12666 | 61 |